I don't really see that a bait that is trotted down a swim that slows/speeds up a tiny amount will stop a fish that is competing with others from taking the bait, if they want it they just haven't the time to inspect it.
The only trotting I have done has been with a fixed spool reel, it didn't seem that difficult and I caught plenty of fish including chub of around 4lbs I might have caught more if I was better at it but really is it that difficult?
It's not about the bait being taken in the first place, it's about getting the bait to a certain point and retaining enough control to be able to hit the resulting bite. This is only exacerbated when trotting at distance or in turbulent and shifting water. I find that I need to do minimal mending of the line with a centrepin than I would with a fixed spool reel. To a less dramatic extent, the same is true of a true pin over a bearing reel.
If you genuinely believe that it makes no difference, then there's little point in using a pin over a fixed spool reel. You are just making life unnecessarily difficult for yourself. Judging by the relative scarcity of centrepin users, many folks undoubtedly do feel that way. For my part, I value the close float control that a centrepin can offer. If a minor difference between pins can offer even closer control, all the better for me.
I managed perfectly well for years using closed face and fixed spool reels. However, I'm quite content that centrepins have contributed to me being able to hit extra fish. It's a bonus that I also happen to enjoy using them. I doubt that anyone is denying that fish can be caught using a fixed spool reel, or any old pin, but that's quite different to suggesting that there's no difference between them.
It's the same with rods. You can catch fish on any old rod. A broom handle will do it if it's long enough. However, if you've a mind, you can catch even more with a better rod, or one that's more suitable for the job in hand. In exactly the same way, some folks will deny that there can be any differences between rods.